The chirp modulation method is a modulation method in which the frequency of a signal (chirp) varies linearly over time in a bandwidth of Fs Hz. A chirp having a positive gradient in the frequency-time plane is generally referred to as an up-chirp, for example chirp 1 and chirp 2 on FIG. 1. A chirp having a negative gradient in the frequency-time plane is generally referred to as a down-chirp, for example chirp 3 on FIG. 1.
A chirp can be represented by a sequence of N samples. One or more identical contiguous chirps can form a symbol that represents a data value to be communicated. A chirp can be represented mathematically as:C(g,p)=ejπg(n-fn(p))(n+1-fn(p))/N  (equation 1)where g is the gradient of the chirp, N is the number of samples in the sequence, n is a sample in the sequence, p is a symbol value, fn(p) is a function that encodes p onto the received chirp, which implicitly may also be a function of g, n, N and other constants, and C is the received chirp sequence, which is normally evaluated for all integer values of n from 0 to N−1 in order. The number of valid values of p is the symbol set size, which is nominally N. However, the symbol set size can be more or less than N depending on the quality of the link. The value of g can have any value greater than 0 and less than N. Preferably, g is an integer between 1 and N−1. Due to the modular nature of this expression negative gradients are obtained from N−1 backwards. Hence, N−2 is equivalent to a negative gradient of −2. Where there are more than one identical contiguous chirps in a symbol, each chirp individually conveys the same value which is the symbol value of the symbol.
Chirp 1 in FIG. 1 has a starting frequency of −Fs/2 and a gradient of 1. It increases linearly in frequency over a period of N samples at a sample rate of Fs to reach a frequency close to +Fs/2. Since this is a complex sampled system +Fs/2 is the same as −Fs/2. Multiple chirps are usually contiguous but may start with a different frequency. The signal phase is typically made continuous throughout a sequence of chirps. In other words, after the signal has reached +Fs/2 at n=N−1, the next symbol starts with n=0 again. FIG. 1 illustrates an example in which two consecutive chirps have the same symbol value, whereas the third chirp is different. An apparent discontinuity in frequency between chirp 1 and chirp 2 occurs at n=N.
Chirp 4 in FIG. 2 has a gradient of 2 and a starting frequency of −Fs/2. Because it has double the gradient of the chirps of FIG. 1, it increases linearly in frequency to +Fs/2 in half the number of samples that the chirps in FIG. 1 do, i.e. it reaches close to +Fs/2 after close to N/2 samples. The chirp then wraps around in frequency. Since this is a sampled system, these frequency wraps are in effect continuous and have continuous phase. The chirp repeats the frequency sweep from −Fs/2 to +Fs/2 between samples N/2 and N.
The chirps also have continuous frequency and phase from one end of the chirp to the other. A cyclic shift of the samples that make up a chirp creates another valid chirp.
Chirp communications are typically used in low cost, battery powered systems operating using low data rates and short messages, often in noisy environments or over long distances. As a result of these constraints every transmitted data bit is valuable. Irregular control data reduces the efficiency of the communication. Thus, a method for transmitting more data within a given bandwidth and a means to manage irregular control data is desirable.
For example, when two devices are communicating with an agreed data rate and quality of service (QoS) it is desirable that each transmitted symbol is as long as possible to enhance its likelihood of being received correctly. Hence, during normal operation it is desirable for the main payload information to fully occupy the available transmit time for the duration of the connection. However, there may be occasions when additional control information also needs to be transmitted, for example to change power levels, adjust the link quality, provide additional parity bits for sensitive symbols or to indicate that a frame needs to be retransmitted. This additional information is generally transmitted much less frequently than the payload information and may not necessarily be transmitted regularly. In a conventional communication system provision is made for control information in the form of additional control packets that are exchanged between devices, often at regular intervals. In one method, these control packets are embedded serially in between payload packets using time division multiple access (TDMA). In this case less time is available for the payload packets and hence more power is required for the same receiver sensitivity. In a second method, control packets are transmitted at the same time as the payload packets but use a different frequency, for example utilising frequency division multiple access (FDMA). In this case more spectral resources, more battery power and a more complicated radio are required, which is not consistent with a very cheap and low power receiver. In a third method, control packets are transmitted at the same time and the same frequency as the payload packets but use a coding scheme, such as code division multiple access (CDMA). In this case the receiver suffers crosstalk interference between the payload packets and the overlaid control packets. This method thus requires additional power for the payload packets to achieve the same receiver sensitivity. It also requires more power to transmit the additional control packets. CDMA receivers are also expensive.
Thus, there is a need for an improved method of communicating a chirp signal from a transmitter to a receiver that is spectrally efficient and provides a means to convey irregular control information without a significant power or delay penalty on the payload information.